"Endurance of civilizations" is the key parameter here. The universe is almost 14 billion years old. Colonizing the Milky Way only takes 1 million years if you can travel 10% of the speed of light. So time and distance aren't significant obstacles for a highly enduring civilization.
Given our massive uncertainty about the endurance/motives/etc. of super-advanced starfaring civiliations, I don't think it's justified to say that alien interlopers are "vanishingly unlikely".
Given our massive uncertainty about the endurance/motives/etc. of super-advanced starfaring civiliations, I don't think it's justified to say that alien interlopers are "vanishingly unlikely".